Ad rendering parameters, such as size, style, and/or layout, of online ads

ABSTRACT

Ad rendering parameters for a set of two or more ads may be determined by (a) accepting, for a set of two or more ads, ad information which includes at least one ad feature having a value that depends on ad rendering parameters, and (b) determining ad rendering parameters for at least one ad from the set of two or more ads using the accepted ad information. The act of determining ad rendering parameters may use accepted ad rendering constraints. The ad rendering constraints may include space available for rendering the ads, a footprint available for rendering the ads, and/or a maximum number of ads permitted to be rendered. The act of determining ad rendering parameters may include maximizing a value associated with serving at least one ad from the set of two or more ads with ad rendering parameters subject to the ad rendering constraints. The ad rendering parameters may include sizes of the served ads, and/or a layout of the served ads.

§ 1. BACKGROUND OF THE INVENTION § 1.1 Field of the Invention

The present invention concerns online advertising. In particular, thepresent invention concerns improving the size and/or layout of onlineads.

§ 1.2 Background Information

Traditional online, tabular yellow page listings have some limitations.For example, since they are all the same size, they can't convey animplicit message to the user about how much money the company can affordto spend on ads and, therefore, how large it may be (larger companiesoften being thought of as more reliable). Further, some may find them tobe difficult to read because of limited typefaces. Furthermore, mosthave little or no additional information on products carried by thecompany because of limited sizes.

In view of the foregoing, it would be useful to improve online ads.

§ 2. SUMMARY OF THE INVENTION

Embodiments consistent with the present invention may determine adrendering parameters for a set of two or more ads by (a) accepting, fora set of two or more ads, ad information, wherein the ad informationincludes at least one ad feature having a value that depends on adrendering parameters, and (b) determining ad rendering parameters for atleast one ad from the set of two or more ads using the accepted adinformation.

At least some embodiment consistent with the present invention mayaccept ad rendering constraints, wherein the act of determining adrendering parameters further uses the accepted ad rendering constraints.In at least some such embodiments, the ad rendering constraints mayinclude space available for rendering the ads, a footprint available forrendering the ads, and/or a maximum number of ads permitted to berendered.

In at least some embodiments consistent with the present invention, theact of determining ad rendering parameters includes maximizing a valueassociated with serving at least one ad from the set of two or more adswith ad rendering parameters subject to the ad rendering constraints.

In at least some embodiments consistent with the present invention, thead rendering parameters may include sizes of the served ads, and/or alayout of the served ads

§ 3. BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing parties or entities that can interact withan advertising system.

FIG. 2 is a diagram illustrating an exemplary environment in which, orwith which, the present invention may operate.

FIG. 3 is a bubble diagram of exemplary operations for determining adparameters which may be performed in a manner consistent with thepresent invention, as well as information that may be used and/orgenerated by such operations.

FIG. 4 is a flow diagram of an exemplary method for performing an ad andad parameter determination operation in a manner consistent with thepresent invention

FIG. 5 is a block diagram of apparatus that may be used to perform atleast some operations, and store at least some information, consistentwith the present invention.

FIGS. 6-8 illustrate exemplary advertisement layout pages that are usedto illustrate how an exemplary embodiment consistent with the presentinvention may be used to improve ad size and/or layout.

§ 4. DETAILED DESCRIPTION

The present invention may involve novel methods, apparatus, messageformats, and/or data structures for improving online advertising. Thefollowing description is presented to enable one skilled in the art tomake and use the invention, and is provided in the context of particularapplications and their requirements. Thus, the following description ofembodiments consistent with the present invention provides illustrationand description, but is not intended to be exhaustive or to limit thepresent invention to the precise form disclosed. Various modificationsto the disclosed embodiments will be apparent to those skilled in theart, and the general principles set forth below may be applied to otherembodiments and applications. For example, although a series of acts maybe described with reference to a flow diagram, the order of acts maydiffer in other implementations when the performance of one act is notdependent on the completion of another act. Further, non-dependent actsmay be performed in parallel. No element, act or instruction used in thedescription should be construed as critical or essential to the presentinvention unless explicitly described as such. Also, as used herein, thearticle “a” is intended to include one or more items. Where only oneitem is intended, the term “one” or similar language is used. Thus, thepresent invention is not intended to be limited to the embodiments shownand the inventors regard their invention to include any patentablesubject matter described.

In the following definitions of terms that may be used in thespecification are provided in § 4.1. Then, environments in which, orwith which, the present invention may operate are described in § 4.2.Exemplary embodiments of the present invention are described in § 4.3.Thereafter, a specific example illustrating the usefulness of oneembodiment of the present invention is provided in § 4.4. Finally, someconclusions regarding the present invention are set forth in § 4.5.

§ 4.1 Definitions

Online ads, such as those used in the exemplary systems described belowwith reference to FIGS. 1 and 2, or any other system, may have variousintrinsic attributes. Such attributes may be specified by an applicationand/or an advertiser. These attributes are referred to as “adattributes” below. For example, in the case of a text ad, ad attributesmay include a title line, ad text, and an embedded link. In the case ofan image ad, ad attributes may include images, executable code, and anembedded link. Depending on the type of online ad, ad attributes mayinclude one or more of the following: text, a link, an audio file, avideo file, an image file, executable code, embedded information, etc.

When an online ad is served, one or more parameters may be used todescribe how, when, and/or where the ad was served. These parameters arereferred to as “serving parameters” below. Serving parameters mayinclude, for example, one or more of the following: features of(including information on) a page on which the ad was served, a searchquery or search results associated with the serving of the ad, a usercharacteristic (e.g., their geolocation, the language used by the user,the type of browser used, previous page views, previous behavior), ahost or affiliate site (e.g., America Online, Google, Yahoo) thatinitiated the request, an absolute position of the ad on the page onwhich it was served, a position (spatial or temporal) of the ad relativeto other ads served, an absolute size of the ad, a size of the adrelative to other ads, a color of the ad, a number of other ads served,types of other ads served, time of day served, time of week served, timeof year served, on what basis the ad was determined relevant, etc.Naturally, there are other serving parameters that may be used in thecontext of the invention.

“Ad rendering parameters” may include the size(s) of one or more ads,the layout of one or more ads, the styles of one or more ads, etc.“Styles ” may include font types, font sizes, background color,foreground color, distance and extent of audio/image/animation/video,etc.

Although serving parameters may be extrinsic to ad attributes, they maybe associated with an ad as serving conditions or constraints. When usedas serving conditions or constraints, such serving parameters arereferred to simply as “serving constraints” (or “targeting criteria”).For example, in some systems, an advertiser may be able to target theserving of its ad by specifying that it is only to be served onweekdays, no lower than a certain position, only to users in a certaingeolocation, etc. As another example, in some systems, an advertiser mayspecify that its ad is to be served only if a page or search queryincludes certain keywords or phrases (referred to generally as “keywordtargeting criteria”). As yet another example, in some systems, anadvertiser may specify that its ad is to be served only if a documentbeing served includes certain topics or concepts, or falls under aparticular cluster or clusters, or some other classification orclassifications.

“Ad information” may include any combination of ad attributes, adserving constraints, information derivable from ad attributes or adserving constraints (referred to as “ad derived information”), and/orinformation related to the ad (referred to as “ad related information”),as well as an extension of such information (e.g., information derivedfrom ad related information).

A “document” is to be broadly interpreted to include anymachine-readable and machine-storable work product. A document may be afile, a combination of files, one or more files with embedded links toother files, etc. The files may be of any type, such as text, audio,image, video, etc. Parts of a document to be rendered to, or perceivedby, an end user can be thought of as “content” of the document. Adocument may include “structured data” containing both content (words,pictures, etc.) and some indication of the meaning of that content (forexample, e-mail fields and associated data, HTML tags and associateddata, etc.) Ad spots in the document may be defined by embeddedinformation or instructions. In the context of the Internet, a commondocument is a Web page. Web pages often include content and may includeembedded information (such as meta information, hyperlinks, etc.) and/orembedded instructions (such as Javascript, etc.). In many cases, adocument has a unique, addressable, storage location and can thereforebe uniquely identified by this addressable location. A universalresource locator (URL) is a unique address used to access information onthe Internet.

“Document information” may include any information included in thedocument, information derivable from information included in thedocument (referred to as “document derived information”), and/orinformation related to the document (referred to as “document relatedinformation”), as well as an extensions of such information (e.g.,information derived from related information). An example of documentderived information is a classification based on textual content of adocument. Examples of document related information include documentinformation from other documents with links to the instant document, aswell as document information from other documents to which the instantdocument links.

Content from a document may be rendered on a “content renderingapplication or device”. Examples of content rendering applicationsinclude an Internet browser (e.g., Explorer or Netscape), a media player(e.g., an MP3 player, a Realnetworks streaming audio file player, etc.),a viewer (e.g., an Abobe Acrobat pdf reader), etc.

“User information” may include user behavior information and/or userprofile information. It may also include a user's geolocation, or anestimation of the user's geolocation.

“E-mail information” may include any information included in an e-mail(also referred to as “internal e-mail information”), informationderivable from information included in the e-mail and/or informationrelated to the e-mail, as well as extensions of such information (e.g.,information derived from related information). An example of informationderived from e-mail information is information extracted or otherwisederived from search results returned in response to a search querycomposed of terms extracted from an e-mail subject line. Examples ofinformation related to e-mail information include e-mail informationabout one or more other e-mails sent by the same sender of a givene-mail, or user information about an e-mail recipient. Informationderived from or related to e-mail information may be referred to as“external e-mail information.”

§ 4.2 Environments in Which, or With Which, the Present Invention MayOperate § 4.2.1 Exemplary Advertising Environment

FIG. 1 is a diagram of an advertising environment 100. The environment100 may include an ad entry, maintenance and delivery system (simplyreferred to as an “ad server”) 120. Advertisers 110 may directly, orindirectly, enter, maintain, and track ad information in the system 120.The ads may be in the form of graphical ads such as so-called bannerads, text only ads, image ads, audio ads, video ads, ads combining oneof more of any of such components, etc. The ads may also includeembedded information, such as a link, and/or machine executableinstructions. Ad consumers 130 may submit requests for ads to, acceptads responsive to their request from, and provide usage information to,the system 120. An entity other than an ad consumer 130 may initiate arequest for ads. Although not shown, other entities may provide usageinformation (e.g., whether or not a conversion or click-through relatedto the ad occurred) to the system 120. This usage information mayinclude measured or observed user behavior related to ads that have beenserved.

The ad server 120 may be similar to the one described in FIG. 2 of U.S.patent application Ser. No. 10/375,900 (incorporated herein byreference), entitled “SERVING ADVERTISEMENTS BASED ON CONTENT,” filed onFeb. 26, 2003 and listing Darrell Anderson, Paul Bucheit, Alex Carobus,Claire Cui, Jeffrey A. Dean, Georges R. Harik, Deepak Jindal, andNarayanan Shivakumar as inventors. An advertising program may includeinformation concerning accounts, campaigns, creatives, targeting, etc.The term “account” relates to information for a given advertiser (e.g.,a unique e-mail address, a password, billing information, etc.). A“campaign” or “ad campaign” refers to one or more groups of one or moreadvertisements, and may include a start date, an end date, budgetinformation, geo-targeting information, syndication information, etc.For example, Honda may have one advertising campaign for its automotiveline, and a separate advertising campaign for its motorcycle line. Thecampaign for its automotive line may have one or more ad groups, eachcontaining one or more ads. Each ad group may include targetinginformation (e.g., a set of keywords, a set of one or more topics,geolocation information, user profile information, etc.), and priceinformation (e.g., maximum cost (cost per click-though, cost perconversion, etc.)). Alternatively, or in addition, each ad group mayinclude an average cost (e.g., average cost per click-through, averagecost per conversion, etc.). Therefore, a single maximum cost and/or asingle average cost may be associated with one or more keywords, and/ortopics. As stated, each ad group may have one or more ads or “creatives”(That is, ad content that is ultimately rendered to an end user.). Eachad may also include a link to a URL (e.g., a landing Web page, such asthe home page of an advertiser, or a Web page associated with aparticular product or server). Naturally, the ad information may includemore or less information, and may be organized in a number of differentways.

FIG. 2 illustrates an exemplary environment 200 in which, or with which,the present invention may be used. A user device (also referred to as a“client” or “client device”) 250 may include a browser facility (such asthe Explorer browser from Microsoft, the Opera Web Browser from OperaSoftware of Norway, the Navigator browser from AOL/Time Warner, theFirefox browser from the Mozilla, etc.), an e-mail facility (e.g.,Outlook from Microsoft), etc. A search engine 220 may permit userdevices 250 to search collections of documents (e.g., Web pages). Acontent server 210 may permit user devices 250 to access documents. Ane-mail server (such as GMail from Google, Hotmail from MicrosoftNetwork, Yahoo Mail, etc.) 240 may be used to provide e-mailfunctionality to user devices 250. An ad server 210 may be used to serveads to user devices 250. The ads may be served in association withsearch results provided by the search engine 220. However,content-relevant ads may be served in association with content providedby the content server 230, and/or e-mail supported by the e-mail server240 and/or user device e-mail facilities.

As discussed in U.S. patent application Ser. No. 10/375,900 (introducedabove), ads may be targeted to documents served by content servers.Thus, one example of an ad consumer 130 is a general content server 230that receives requests for documents (e.g., articles, discussionthreads, music, video, graphics, search results, Web page listings,etc.), and retrieves the requested document in response to, or otherwiseservices, the request. The content server may submit a request for adsto the ad server 120/210. Such an ad request may include a number of adsdesired. The ad request may also include document request information.This information may include the document itself (e.g., page), acategory or topic corresponding to the content of the document or thedocument request (e.g., arts, business, computers, arts-movies,arts-music, etc.), part or all of the document request, content age,content type (e.g., text, graphics, video, audio, mixed media, etc.),geo-location information, document information, etc.

The content server 230 may combine the requested document with one ormore of the advertisements provided by the ad server 120/210. Thiscombined information including the document content and advertisement(s)is then forwarded towards the end user device 250 that requested thedocument, for presentation to the user. Finally, the content server 230may transmit information about the ads and how, when, and/or where theads are to be rendered (e.g., position, click-through or not, impressiontime, impression date, size, conversion or not, etc.) back to the adserver 120/210. Alternatively, or in addition, such information may beprovided back to the ad server 120/210 by some other means.

Another example of an ad consumer 130 is the search engine 220. A searchengine 220 may receive queries for search results. In response, thesearch engine may retrieve relevant search results (e.g., from an indexof Web pages). An exemplary search engine is described in the article S.Brin and L. Page, “The Anatomy of a Large-Scale Hypertextual SearchEngine,” Seventh International World Wide Web Conference, Brisbane,Australia and in U.S. Pat. No. 6,285,999 (both incorporated herein byreference). Such search results may include, for example, lists of Webpage titles, snippets of text extracted from those Web pages, andhypertext links to those Web pages, and may be grouped into apredetermined number of (e.g., ten) search results.

The search engine 220 may submit a request for ads to the ad server120/210. The request may include a number of ads desired. This numbermay depend on the search results, the amount of screen or page spaceoccupied by the search results, the size and shape of the ads, etc. Inone embodiment, the number of desired ads will be from one to ten, andpreferably from three to five. The request for ads may also include thequery (as entered or parsed), information based on the query (such asgeolocation information, whether the query came from an affiliate and anidentifier of such an affiliate, and/or as described below, informationrelated to, and/or derived from, the search query), and/or informationassociated with, or based on, the search results. Such information mayinclude, for example, identifiers related to the search results (e.g.,document identifiers or “docIDs”), scores related to the search results(e.g., information retrieval (“IR”) scores such as dot products offeature vectors corresponding to a query and a document, Page Rankscores, and/or combinations of IR scores and Page Rank scores), snippetsof text extracted from identified documents (e.g., Web pages), full textof identified documents, topics of identified documents, feature vectorsof identified documents, etc.

The search engine 220 may combine the search results with one or more ofthe advertisements provided by the ad server 120/210. This combinedinformation including the search results and advertisement(s) is thenforwarded towards the user that submitted the search, for presentationto the user. Preferably, the search results are maintained as distinctfrom the ads, so as not to confuse the user between paid advertisementsand presumably neutral search results.

Finally, the search engine 220 may transmit information about the ad andwhen, where, and/or how the ad was to be rendered (e.g., position,click-through or not, impression time, impression date, size, conversionor not, etc.) back to the ad server 120/210. As described below, suchinformation may include information for determining on what basis the adway determined relevant (e.g., strict or relaxed match, or exact,phrase, or broad match, etc.) Alternatively, or in addition, suchinformation may be provided back to the ad server 120/210 by some othermeans.

Finally, the e-mail server 240 may be thought of, generally, as acontent server in which a document served is simply an e-mail. Further,e-mail applications (such as Microsoft Outlook for example) may be usedto send and/or receive e-mail. Therefore, an e-mail server 240 orapplication may be thought of as an ad consumer 130. Thus, e-mails maybe thought of as documents, and targeted ads may be served inassociation with such documents. For example, one or more ads may beserved in, under over, or otherwise in association with an e-mail.

Although the foregoing examples described servers as (i) requesting ads,and (ii) combining them with content, one or both of these operationsmay be performed by a client device (such as an end user computer forexample).

§ 4.3 Exemplary Embodiments

FIG. 3 is a bubble diagram of exemplary operations which may beperformed in a manner consistent with the present invention, as well asinformation that may be used and/or generated by such operations. Ad andad parameter determination operations 350 may be used to determinerendering parameters (e.g., sizes, layouts, and/or styles) for onlineads. The layouts are not limited to a simple linear list of results. Forexample_(;) layouts of the ads may be more similar to page layouts usedin yellow pages.

The ad and ad parameter determination operations 350 may use adinformation 310, query information (which may include user information)320, and/or constraint information 330 to determine a set of ads andtheir parameters 360. Ad information 310 may include ad features 340having “values” that depend on ad rendering parameters. Further adinformation 310 may include one or more of offer information (e.g.,price per impression, selection or conversion, maximum offer perimpression, selection or conversion, etc.), location information,product information, targeting information, performance information(e.g., selection rate, conversion rate, etc.), etc. Query information320 may include one or more of search terms, content topics, end userlocation or location of interest, user profile, user behavior, etc.

Constraint information 330 may include one or more of screen space (orfootprint) for the ads, maximum number of ads permitted, etc.

The constraint information 330 and ad features 340 may be used todetermine ads and their rendering parameters. Query information 320and/or other ad information 310 may also be used in this determination.Thus, the operations 350 can be used to determine a “best” combinationof size, style, and/or layout of ads.

§ 4.3.1 Exemplary Methods

FIG. 4 is a flow diagram of an exemplary method 400 that may be used toperform ad rendering parameter (and perhaps ad) determination operationsin a manner consistent with the present invention. The method 400 mayaccept a variety of information to determine an optimized set ofrendered ads. In particular, the method 400 may accept ad information(that includes at least one ad feature having a “value” that depends onad rendering parameters) (Block 405), query information (Block 410),and/or constraint information (Block 415). This obtained information maythen be processed to determine an optimized set of ads, including theirrendering parameters (Block 420).

Examples of ad information, query information, and constraintinformation were described earlier in § 4.3. Hence, exemplary featurevalues will be described here. As described above with reference toblock 420, ad rendering parameter determination method 400 may accept adfeatures having values that depend on the ad rendering parameters. Thesead features are used by the method 400 to define a constrainedoptimization problem where the optimum rendering parameters (e.g., size,style, and/or layout) of ads are determined. (Block 420) Features thatmay be used to optimize the ad rendering parameters, may include:features having a value that depends on ad rendering parameters (such asselection rate, conversion rate, offer for impression, offer forselection, offer for conversion, ad size (absolute or relative), adstyle (absolute or relative), ad layout, etc).

Referring back to block 420, an example of an optimization problem maybe defined as maximizing a weighted combination of the feature valuesfor an advertisement relative to the size of the ad. The number offeatures, constraints, and calculations that may be involved in such aconstrained optimization function may be very large and complex.Therefore, standard methods of solving such problems (e.g., linearprogramming, non-linear programming, integer programming, simulatedannealing, etc.) can be used as appropriate (depending on the sort ofadditional constraints used). A simple constrained optimization problemwill be described in § 4.4 below.

§ 4.3.2 Exemplary Apparatus

FIG. 5 is high-level block diagram of a machine 500 that may perform oneor more of the operations discussed above. The machine 500 basicallyincludes one or more processors 510, one or more input/output interfaceunits 530, one or more storage devices 520, and one or more system busesand/or networks 540 for facilitating the communication of informationamong the coupled elements. One or more input devices 532 and one ormore output devices 534 may be coupled with the one or more input/outputinterfaces 530.

The one or more processors 510 may execute machine-executableinstructions (e.g., C or C++ running on the Solaris operating systemavailable from Sun Microsystems Inc. of Palo Alto, Calif. or the Linuxoperating system widely available from a number of vendors such as RedHat, Inc. of Durham, N.C.) to perform one or more aspects of the presentinvention. At least a portion of the machine executable instructions maybe stored (temporarily or more permanently) on the one or more storagedevices 520 and/or may be received from an external source via one ormore input interface units 530.

In one embodiment, the machine 500 may be one or more conventionalpersonal computers. In this case, the processing units 510 may be one ormore microprocessors. The bus 540 may include a system bus. The storagedevices 520 may include system memory, such as read only memory (ROM)and/or random access memory (RAM). The storage devices 520 may alsoinclude a hard disk drive for reading from and writing to a hard disk, amagnetic disk drive for reading from or writing to a (e.g., removable)magnetic disk, and an optical disk drive for reading from or writing toa removable (magneto-) optical disk such as a compact disk or other(magneto-) optical media.

A user may enter commands and information into the personal computerthrough input devices 532, such as a keyboard and pointing device (e.g.,a mouse) for example. Other input devices such as a microphone, ajoystick, a game pad, a satellite dish, a scanner, or the like, may also(or alternatively) be included. These and other input devices are oftenconnected to the processing unit(s) 510 through an appropriate interface530 coupled to the system bus 540. The output devices 534 may include amonitor or other type of display device, which may also be connected tothe system bus 540 via an appropriate interface. In addition to (orinstead of) the monitor, the personal computer may include other(peripheral) output devices (not shown), such as speakers and printersfor example.

§ 4.3.3 Refinements and Alternatives

Although many of the foregoing discussions and examples concerndetermining rendering parameters (e.g., styles, sizes, and/or layouts(e.g., yellow page-like layouts)) for ads, there are many otherapplications in which the principles of the present invention could beapplied. For instance, embodiments consistent with the present inventioncould be used for determining the layout of news stories. For example,the amount of space and size of the font for the news headline could becontrolled by a similar method. Also, embodiments consistent with thepresent invention could be refined to support the creation of dynamicyellow book-like pages that work with concept-targeted ads rather thankeyword-targeted ads. For instance, if a user conducts a search on thekey-word “plumbers”, instead of just providing a list of plumbers, itcould also provide a list of hardware stores.

Furthermore, the invention may be able to further refine the optimizedad sizes and layout by using a variety of optimization algorithms (VLSIlayout, stochastic search, dynamic programming, etc.) to determineplacement alternatives and may further refine the weights used in theoptimization over time, using ad selection rate for different media,different locations, and/or different classes of users.

Another refinement can be to provide constraints as to how ads withdifferent sizes and shapes can be mixed with respect to one another,thereby preventing a layout that is jumbled (e.g., due to too many sizeson the layout, ad size set discontinuities, etc.). For instance, oncesizes for each ad are determined by the methods discussed earlier, theinvention can then quantize the ads as necessary to fit the “closest”available ad size. Such quantization can be incorporated into theoriginal optimization problem through additional constraints.

Computations taking place during the operations of the present inventionmay be complicated and extensive. However, other common methods fortackling non-linear result sets may be used, such as showing atopographic map.

§ 4.4 Example Of Operations

FIGS. 6-8 illustrate exemplary candidate layouts for displaying yellowpage-like ads, used to illustrate exemplary operations in an exemplaryembodiment of the invention. FIGS. 6-8 serve as layout constraints to anoptimization problem since only three (3) ads can be displayed on eachlayout, and each ad must fit to one of the spaces defined in a layout.In FIG. 6 since the allotted space for ads has been divided evenly intothree pieces, each ad will have a size of one third of the totalallotted space allowed for ads. In FIG. 7 each ad could be sized to fitin any of the three (3) divided spaces. Hence, one (1) of the ads couldhave a size of one half, while the other two (2) ads would have a sizeof one fourth. In FIG. 8, again each ad could be sized to fit in any ofthree (3) divided spaces. Hence, one of the ads could have a size of twothirds, while the other two (2) ads would have a size of one sixth.Thus, there are three potential layouts for the ads to be displayed on,and one of five possible sizes each ad could have. These possibleparameters serve as constraints to the following example.

In the following, a detailed example of the optimization operation thatmay occur at the ad and ad parameter determination operation will bepresented. In particular, the optimization problem concerns maximizing aconstrained function of weighted combinations of feature values for anadvertisement relative to the size of the ad.

Specifically, consider having a set of advertisers who are targeting thequery “leather jacket”. Each of these advertisers has some featuresassociated with them. Consider the following advertisers:

-   Advertiser_1: Macy's-   Distance: 0.1-   CTR: 0.05*size of ad

Advertiser_2: Nordstrom

-   Distance: 0.3-   CTR: 0.03*size of ad-   Advertiser_3: Target-   Distance: 0.9-   CTR: 0.06*size of ad

The feature values from these advertisers are distance and CTR(click-through rate) and are represented by the following:

-   Feature_val_1=Distance-   Feature_val_2=CTR

Here, distance refers to the distance from the user to the advertisedlocation and CTR refers to the click-through rate of the ad. No unitsare shown for values of distance since they serve no significance forthis illustration (they could be miles, kilometers, etc). Also note thatthe click-through rate is a linear function of the size of the ad whichis the variable to be optimized.

Now consider the optimization problem of maximizing the function:

${\sum\limits_{\alpha}{\sum\limits_{\lambda}\left( {{weight\_\lambda} \times {Feature\_ val}{\_\lambda} \times {size\_\alpha}} \right)}} + {\sum\limits_{\gamma}({reward\_\gamma})}$

where α is an index of ads, λ is an index of features and γ is an indexof conditions, subject to the following constraints:

${\sum\limits_{\alpha}({size\_\alpha})} = 1$${{size\_\alpha} \geq \frac{1}{\kappa}},{\forall{\alpha \in \left\lbrack {1,3} \right\rbrack}}$

-   -   where κ is a constant and κ≥(number of ads). In this case, κ=6        since the smallest size available on the three layouts depicted        by FIGS. 6-8 is one sixth.

Also, consider the additional constraints mentioned earlier depicted byFIGS. 6-8. In particular, only three (3) ads can be displayed on eachlayout, and each ad must fit to one of the divided spaces from a layout.Thus, there are three potential layouts and one of five possible sizeseach ad could have.

Note that some implementations could involve a large number of featuresand constraints in the optimization problem, making it computationallyexpensive. However, this simple example is useful for purposes ofillustration.

In the above optimization problem weight_λ denotes the weight of theλ^(th) feature of an ad, Feature val_λ denotes the value of the λ^(th)feature for the ad, and size_α denotes the size of an ad. Specifically,α=1 refers to advertiser_1, α=2 refers to advertiser_2, and α=3 refersto advertiser_3.

The following exemplary weights are assigned to each feature. SinceFeature_val_1 depends on distance, a function that decreases values asthe distance between the user and the advertised location increases isused.

Hence a possible weight function may be:

${{weight\_}1} = {\frac{30}{\left( {{distance} + 0.5} \right)}.}$

This weight function will be assigned to Feature_val_1 and will be usedin this example. The weight given to Feature_val_2 which refers to theclick-through weight of an ad will be defined as a constantspecifically, weight_2=100.

Furthermore, the reward_γ included in the optimization problem denotes areward given for satisfying condition γ. The reward values and theirrespective conditions can be represented by the function_satisfied_γwhich indicates the degree to which condition γ is satisfied.

Specifically, in this example, the rewards are defined as follows:

γ=1(refers to advertiser_1)⇒function_satisfied_1:

If size_1≥0.5, then reward_1=5 else reward_1=0.

γ=2 (refers to advertiser_2)⇒function_satisfied_2:

If size_2≥0.25, then reward_2=3 else reward_2=0.

γ=3 (refers to advertiser_3)⇒function_satisfied_3:

If size_3≥1/3, then reward_3=4 else reward_3=0.

The above conditions and results can be thought of as additionalconstraints of the optimization problem.

Having defined all features, weights, constraints, as well as a functionto maximize, the optimization problem can now be solved. Again the goalis to maximize the constrained function:

${\sum\limits_{\alpha}{\sum\limits_{\lambda}\left( {{weight\_\lambda} \times {Feature\_ val}{\_\lambda} \times {size\_\alpha}} \right)}} + {\sum\limits_{\gamma}{({reward\_\gamma}).}}$

A series of calculations will follow:

1^(ST) Layout (FIG. 6):

For

$\left. \begin{matrix}{{{size\_}1} = \frac{1}{3}} \\{{{size\_}2} = \frac{1}{3}} \\{{{size\_}3} = \frac{1}{3}}\end{matrix} \right\},$

entering these values in the optimization function generates:According to equation

${\sum\limits_{\alpha}{\sum\limits_{\lambda}\left( {{weight\_\lambda} \times {Feature\_ val}{\_\lambda} \times {size\_\alpha}} \right)}} + {\sum\limits_{\gamma}({reward\_\gamma})}$

For α=1 (advertiser_1):

-   -   For λ=1 (first feature value), γ=1 (refers to advertiser_1):

(weight_1×Feature_val_1×size_1)+0   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}1} \right)} & (2) \\{\mspace{79mu} \left. {(1) + (2)}\Rightarrow {\left( {\left( \frac{30}{0.1 + 0.5} \right) \times 0.1 \times {size\_}1} \right) + \left( {100 \times 0.05 \times {size\_}1 \times {size\_}1} \right)}\Rightarrow{{5 \times \left( {{size\_}1} \right)} + {5 \times \left( {{size\_}1} \right)^{2}}} \right.} & (a)\end{matrix}$

For α=2 (advertiser_2):

-   -   For λ=1 (first feature value), γ=2 (refers to advertiser_2):

(weight_1×Feature_val_1×size_2)+3   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}2} \right)} & (2) \\{\mspace{79mu} \left. {(1) + (2)}\Rightarrow {\left( {\left( \frac{30}{0.3 + 0.5} \right) \times 0.3 \times {size\_}2} \right) + \left( {100 \times 0.03 \times {size\_}2 \times {size\_}2} \right) + 3}\Rightarrow{{11.25 \times \left( {{size\_}2} \right)} + {3 \times \left( {{size\_}2} \right)^{2}} + 3} \right.} & (b)\end{matrix}$

For α=3 (advertiser_3):

-   -   For λ=1 (first feature value), γ=3 (refers to advertiser_3):

(weight_1×Feature_val_1×size_3)+4   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}3} \right)} & (2) \\{\mspace{79mu} \left. {(1) + (2)}\Rightarrow {\left( {\left( \frac{30}{0.9 + 0.5} \right) \times 0.9 \times {size\_}3} \right) + \left( {100 \times 0.06 \times {size\_}3 \times {size\_}3} \right) + 4}\Rightarrow{{19.29 \times \left( {{size\_}3} \right)} + {6 \times \left( {{size\_}3} \right)^{2}} + 4} \right.} & (c)\end{matrix}$

Summing parts (a)+(b)+(c) provides:

5×(size_1)+5×(size_1)²+11.25×(size_2)+3×(size_2)²+3+19.29×(size_3)+6×(size_3)²+4⇒

Substituting the size values for this orientation and layout provides:

value=20.40

2^(ND) Layout (FIG. 7):

first orientation of ads

For

$\left. \begin{matrix}{{{size\_}1} = \frac{1}{2}} \\{{{size\_}2} = \frac{1}{4}} \\{{{size\_}3} = \frac{1}{4}}\end{matrix} \right\},$

entering these values in the optimization function generates:According to equation

${\sum\limits_{\alpha}\; {\sum\limits_{\lambda}\left( {{weight\_\lambda} \times {Feature\_ val}{\_\lambda} \times {size\_\alpha}} \right)}} + {\sum\limits_{\gamma}({reward\_\gamma})}$

For α=1 (advertiser_1):

-   -   For λ=1 (first feature value), γ=1 (refers to advertiser_1):

(weight_1×Feature_val_1×size_1)+5   (1)

For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}1} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.1 + 0.5} \right) \times 0.1 \times {size\_}1} \right) + \left( {100 \times 0.05 \times {size\_}1 \times {size\_}1} \right) + 5}\Rightarrow{{5 \times \left( {{size\_}1} \right)} + {5 \times \left( {{size\_}1} \right)^{2}} + 5} \right. & (a)\end{matrix}$

For α=2 (advertiser_2):

-   -   For λ=1 (first feature value), γ=2 (refers to advertiser_2):

(weight_1×Feature_val_1×size_2)+3   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}2} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.3 + 0.5} \right) \times 0.3 \times {size\_}2} \right) + \left( {100 \times 0.03 \times {size\_}2 \times {size\_}2} \right) + 3}\Rightarrow{{11.25 \times \left( {{size\_}2} \right)} + {3 \times \left( {{size\_}2} \right)^{2}} + 3} \right. & (b)\end{matrix}$

For α=3 (advertiser_3):

-   -   For λ=1 (first feature value), γ=3 (refers to advertiser_3):

(weight_1×Feature_val_1×size_3)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}3} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.9 + 0.5} \right) \times 0.9 \times {size\_}3} \right) + \left( {100 \times 0.06 \times {size\_}3 \times {size\_}3} \right)}\Rightarrow{{19.29 \times \left( {{size\_}3} \right)} + {6 \times \left( {{size\_}3} \right)^{2}}} \right. & (c)\end{matrix}$

Summing parts (a)+(b)+(c) provides:

5×(size_1)+5×(size_1)²+5+11.25×(size_2)+3×(size_2)²+3+19.29×(size_3)+6×(size_3)²⇒

Substituting the size values for this orientation and layout provides:

value=19.95

second orientation of ads

For

$\left. \begin{matrix}{{{size\_}1} = \frac{1}{4}} \\{{{size\_}2} = \frac{1}{2}} \\{{{size\_}3} = \frac{1}{4}}\end{matrix} \right\},$

entering these values in the optimization function generates:According to equation

${\sum\limits_{\alpha}\; {\sum\limits_{\lambda}\left( {{weight\_\lambda} \times {Feature\_ val}{\_\lambda} \times {size\_\alpha}} \right)}} + {\sum\limits_{\gamma}({reward\_\gamma})}$

For α=1 (advertiser_1):

-   -   For λ=1 (first feature value), γ=1 (refers to advertiser_1):

(weight_1×Feature_val_1×size_1)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}1} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.1 + 0.5} \right) \times 0.1 \times {size\_}1} \right) + \left( {100 \times 0.05 \times {size\_}1 \times {size\_}1} \right)}\Rightarrow{{5 \times \left( {{size\_}1} \right)} + {5 \times \left( {{size\_}1} \right)^{2}}} \right. & (a)\end{matrix}$

For α=2 (advertiser_2):

-   -   For λ=1 (first feature value), γ=2 (refers to advertiser_2):

(weight_1×Feature_val_1×size_2)+3   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}2} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.3 + 0.5} \right) \times 0.3 \times {size\_}2} \right) + \left( {100 \times 0.03 \times {size\_}2 \times {size\_}2} \right) + 3}\Rightarrow{{11.25 \times \left( {{size\_}2} \right)} + {3 \times \left( {{size\_}2} \right)^{2}} + 3} \right. & (b)\end{matrix}$

For α=3 (advertiser_3):

-   -   For λ=1 (first feature value), γ=3 (refers to advertiser_3):

(weight_1×Feature_val_1×size_3)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}3} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.9 + 0.5} \right) \times 0.9 \times {size\_}3} \right) + \left( {100 \times 0.06 \times {size\_}3 \times {size\_}3} \right)}\Rightarrow{{19.29 \times \left( {{size\_}3} \right)} + {6 \times \left( {{size\_}3} \right)^{2}}} \right. & {\;^{\backprime}(c)}\end{matrix}$

Summing parts (a)+(b)+(c) provides:

5×(size_1)+5×(size_1)²+11.25×(size_2)+3×(size_2)²+3+19.29×(size_3)+6×(size_3)²⇒

Substituting the size values for this orientation and layout provides:

value=16.14

third orientation of ads

For

$\left. \begin{matrix}{{{size\_}1} = \frac{1}{4}} \\{{{size\_}2} = \frac{1}{4}} \\{{{size\_}3} = \frac{1}{2}}\end{matrix} \right\},$

entering these values in the optimization function generates:According to equation

${\sum\limits_{\alpha}\; {\sum\limits_{\lambda}\left( {{weight\_\lambda} \times {Feature\_ val}{\_\lambda} \times {size\_\alpha}} \right)}} + {\sum\limits_{\gamma}({reward\_\gamma})}$

For α=1 (advertiser_1):

-   -   For λ=1 (first feature value), γ=1 (refers to advertiser_1):

(weight_1×Feature_val_1×size_1)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}1} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.1 + 0.5} \right) \times 0.1 \times {size\_}1} \right) + \left( {100 \times 0.05 \times {size\_}1 \times {size\_}1} \right)}\Rightarrow{{5 \times \left( {{size\_}1} \right)} + {5 \times \left( {{size\_}1} \right)^{2}}} \right. & (a)\end{matrix}$

For α=2 (advertiser_2):

-   -   For λ=1 (first feature value), γ=2 (refers to advertiser_2):

(weight_1×Feature_val_1×size_2)+3   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}2} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.3 + 0.5} \right) \times 0.3 \times {size\_}2} \right) + \left( {100 \times 0.03 \times {size\_}2 \times {size\_}2} \right) + 3}\Rightarrow{{11.25 \times \left( {{size\_}2} \right)} + {3 \times \left( {{size\_}2} \right)^{2}} + 3} \right. & (b)\end{matrix}$

For α=3 (advertiser_3):

-   -   For λ=1 (first feature value), γ=3 (refers to advertiser_3):

(weight_1×Feature_val_1×size_3)+4   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}3} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.9 + 0.5} \right) \times 0.9 \times {size\_}3} \right) + \left( {100 \times 0.06 \times {size\_}3 \times {size\_}3} \right) + 4}\Rightarrow{{19.29 \times \left( {{size\_}3} \right)} + {6 \times \left( {{size\_}3} \right)^{2}} + 4} \right. & {\; (c)}\end{matrix}$

Summing parts (a)+(b)+(c) provides:

5×(size_1)+5×(size_1)²+11.25×(size_2)+3×(size_2)²+3+19.29×(size_3)+6×(size_3)²+4⇒

Substituting the size values for this orientation and layout provides:

value=22.71

3^(RD) Layout (FIG. 8):

first orientation of ads

For

$\left. \begin{matrix}{{{size\_}1} = \frac{2}{3}} \\{{{size\_}2} = \frac{1}{6}} \\{{{size\_}3} = \frac{1}{6}}\end{matrix} \right\},$

entering these values in the optimization function generates:

According to equation

${\sum\limits_{\alpha}{\sum\limits_{\lambda}\left( {{weight\_\lambda} \times {Feature\_ val}{\_\lambda} \times {size\_\alpha}} \right)}} + {\sum\limits_{\gamma}({reward\_\gamma})}$

For α=1 (advertiser_1):

-   -   For λ=1 (first feature value), γ=1 (refers to advertiser_1):

(weight_1×Feature_val_1×size_1)+5   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}1} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.1 + 0.5} \right) \times 0.1 \times {size\_}1} \right) + \left( {100 \times 0.05 \times {size\_}1 \times {size\_}1} \right) + 5}\Rightarrow{{5 \times \left( {{size\_}1} \right)} + {5 \times \left( {{size\_}1} \right)^{2}} + 5} \right. & (a)\end{matrix}$

For α=2 (advertiser_2):

-   -   For λ=1 (first feature value), γ=2 (refers to advertiser_2):

(weight_1×Feature_val_1×size_2)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}2} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.3 + 0.5} \right) \times 0.3 \times {size\_}2} \right) + \left( {100 \times 0.03 \times {size\_}2 \times {size\_}2} \right)}\Rightarrow{{11.25 \times \left( {{size\_}2} \right)} + {3 \times \left( {{size\_}2} \right)^{2}}} \right. & (b)\end{matrix}$

For α=3 (advertiser_3):

-   -   For λ=1 (first feature value), γ=3 (refers to advertiser_3):

(weight_1×Feature_val_1×size_3)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}3} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.9 + 0.5} \right) \times 0.9 \times {size\_}3} \right) + \left( {100 \times 0.06 \times {size\_}3 \times {size\_}3} \right)}\Rightarrow{{19.29 \times \left( {{size\_}3} \right)} + {6 \times \left( {{size\_}3} \right)^{2}}} \right. & (c)\end{matrix}$

Summing parts (a)+(b)+(c) provides:

5×(size_1)+5×(size_1)²+5+11.25×(size_2)+3×(size_2)²+19.29×(size_3)+6×(size_3)²⇒

Substituting the size values for this orientation and layout provides:

value=15.90

second orientation of ads

For

$\left. \begin{matrix}{{{size\_}1} = \frac{1}{6}} \\{{{size\_}2} = \frac{2}{3}} \\{{{size\_}3} = \frac{1}{6}}\end{matrix} \right\},$

entering these values in the optimization function generates:According to equation

${\sum\limits_{\alpha}{\sum\limits_{\lambda}\left( {{weight\_\lambda} \times {Feature\_ val}{\_\lambda} \times {size\_\alpha}} \right)}} + {\sum\limits_{\gamma}({reward\_\gamma})}$

For α=1 (advertiser_1):

-   -   For λ=1 (first feature value), γ=1 (refers to advertiser_1):

(weight_1×Feature_val_1×size_1)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}1} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.1 + 0.5} \right) \times 0.1 \times {size\_}1} \right) + \left( {100 \times 0.05 \times {size\_}1 \times {size\_}1} \right)}\Rightarrow{{5 \times \left( {{size\_}1} \right)} + {5 \times \left( {{size\_}1} \right)^{2}}} \right. & (a)\end{matrix}$

For α=2 (advertiser_2):

-   -   For λ=1 (first feature value), γ=2 (refers to advertiser_2):

(weight_1×Feature_val_1×size_2)+3   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}2} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.3 + 0.5} \right) \times 0.3 \times {size\_}2} \right) + \left( {100 \times 0.03 \times {size\_}2 \times {size\_}2} \right) + 3}\Rightarrow{{11.25 \times \left( {{size\_}2} \right)} + {3 \times \left( {{size\_}2} \right)^{2}} + 3} \right. & (b)\end{matrix}$

For α=3 (advertiser_3):

-   -   For λ=1 (first feature value), γ=3 (refers to advertiser_3):

(weight_1×Feature_val_1×size_3)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}3} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.9 + 0.5} \right) \times 0.9 \times {size\_}3} \right) + \left( {100 \times 0.06 \times {size\_}3 \times {size\_}3} \right)}\Rightarrow{{19.29 \times \left( {{size\_}3} \right)} + {6 \times \left( {{size\_}3} \right)^{2}}} \right. & (c)\end{matrix}$

Summing parts (a)+(b)+(c) provides:

5×(size_1)+5×(size_1)²+11.25×(size_2)+3×(size_2)²+3+19.29×(size_3)+6×(size_3)²⇒

Substituting the size values for this orientation and layout provides:

value=16.19

third orientation of ads

For

$\left. \begin{matrix}{{{size\_}1} = \frac{1}{6}} \\{{{size\_}2} = \frac{1}{6}} \\{{{size\_}3} = \frac{2}{3}}\end{matrix} \right\},$

entering these values in the optimization function generates:According to equation

${\sum\limits_{\alpha}{\sum\limits_{\lambda}\left( {{weight\_\lambda} \times {Feature\_ val}{\_\lambda} \times {size\_\alpha}} \right)}} + {\sum\limits_{\gamma}({reward\_\gamma})}$

For α=1 (advertiser_1):

-   -   For λ=1 (first feature value), γ=1 (refers to advertiser_1):

(weight_1×Feature_val_1×size_1)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}1} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.1 + 0.5} \right) \times 0.1 \times {size\_}1} \right) + \left( {100 \times 0.05 \times {size\_}1 \times {size\_}1} \right)}\Rightarrow{{5 \times \left( {{size\_}1} \right)} + {5 \times \left( {{size\_}1} \right)^{2}}} \right. & (a)\end{matrix}$

For α=2 (advertiser_2):

-   -   For λ=1 (first feature value), γ=2 (refers to advertiser_2):

(weight_1×Feature_val_1×size_2)   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}2} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.3 + 0.5} \right) \times 0.3 \times {size\_}2} \right) + \left( {100 \times 0.03 \times {size\_}2 \times {size\_}2} \right)}\Rightarrow{{11.25 \times \left( {{size\_}2} \right)} + {3 \times \left( {{size\_}2} \right)^{2}}} \right. & (b)\end{matrix}$

For α=3 (advertiser_3):

-   -   For λ=1 (first feature value), γ=3 (refers to advertiser_3):

(weight_1×Feature_val_1×size_3)+4   (1)

-   -   For λ=2 (second feature value):

$\begin{matrix}{\mspace{79mu} \left( {{weight\_}2 \times {Feature\_ val}\_ 2 \times {size\_}3} \right)} & (2) \\\left. {(1) + (2)}\Rightarrow{\left( {\left( \frac{30}{0.9 + 0.5} \right) \times 0.9 \times {size\_}3} \right) + \left( {100 \times 0.06 \times {size\_}3 \times {size\_}3} \right) + 4}\Rightarrow{{19.29 \times \left( {{size\_}3} \right)} + {6 \times \left( {{size\_}3} \right)^{2}} + 4} \right. & (c)\end{matrix}$

Summing parts (a)+(b)+(c) provides:

5×(size_1)+5×(size_1)²+11.25×(size_2)+3×(size_2)²+19.29×(size_3)+6×(size_3)²+4⇒

Substituting the size values for this orientation and layout provides:

value=22.46

As can be concluded by looking at the generated values in each layout,the optimum configuration is achieved by choosing the second layout(FIG. 7) with the third orientation of ads, which gives value=22.71.

In this configuration advertiser_1 gets an ad space value of two thirdsof the total layout space, advertiser_2 gets an ad space value of onesixth of the total layout space, and advertiser_3 gets an ad space ofone sixth of the total layout space.

§ 4.5 Conclusion

As can be appreciated from the foregoing, the present invention can beused to improve ads by optimizing the size and/or layout of a set ofads.

What is claimed is:
 1. A computer-implemented method comprising: a) fora set of two or more ads, accepting ad information, wherein the adinformation includes at least one ad feature having a value that dependson ad rendering parameters; and b) determining ad rendering parametersfor at least one ad from the set of two or more ads using the acceptedad information.
 2. The computer-implemented method of claim 1 furthercomprising accepting ad rendering constraints, wherein the act ofdetermining ad rendering parameters further uses the accepted adrendering constraints.
 3. The computer-implemented method of claim 2wherein the ad rendering constraints include space available forrendering the ads.
 4. The computer-implemented method of claim 2 whereinthe ad rendering constraints include a footprint available for renderingthe ads.
 5. The computer-implemented method of claim 2 wherein the adrendering constraints include a maximum number of ads permitted to berendered.
 6. The computer-implemented method of claim 2 wherein the actof determining ad rendering parameters includes maximizing a valueassociated with serving at least one ad from the set of two or more adswith ad rendering parameters subject to the ad rendering constraints. 7.The computer-implemented method of claim 1 wherein the ad renderingparameters include sizes of the served ads.
 8. The computer-implementedmethod of claim 1 wherein the ad rendering parameters include a layoutof the served ads.
 9. The computer-implemented method of claim 1 whereinthe ad rendering parameters include styles of the ads
 10. Thecomputer-implemented method of claim 9 wherein the styles of the adsinclude at least one of ad background color and ad foreground color. 11.The computer-implemented method of claim 9 wherein the styles of the adsinclude at least one of font size and font style.
 12. Thecomputer-implemented method of claim 9 wherein the styles of the adsinclude amount of text.
 13. The computer-implemented method of claim 9wherein the styles of the ads include type and degree of graphicalelements.
 14. The computer-implemented method of claim 1 wherein the adinformation includes at least one of language of the ad, ad selectionrate, ad conversion rate, cost of ad, price of items advertised, profiton items being advertised, number of related items that the advertisersells, offer information, location information, product information,targeting information, and performance information.
 15. Thecomputer-implemented method of claim 1 wherein the at least one adfeature having a value that depends on ad rendering parameters is one ofa selection rate and a conversion rate.
 16. The computer-implementedmethod of claim 1 wherein the at least one ad feature having a valuethat depends on ad rendering parameters is one of an offer forimpression, an offer for selection and an offer for conversion.